I dont really understand about interval notations and continuity much. Please sh

Question

I dont really understand about interval notations and continuity much. Please show your work with details in every step. Thank you!

Let f(x) = x - 8/(x - 2)(x + 5) Use interval notation to indicate where f(x) is continuous. NOTE: When using interval notation in WeBWorK, remember that: You use 'I' for infinity and '-I' for - infinity. And use 'U' for the union symbol. Interval(s) of Continuity: Let f(x) = 6x8 - 4x4 + 2. Use interval notation to indicate where f(x) is continuous. NOTE: When using interval notation in WeBWorK, remember that: You use 'I' for infinity and '-I' for - infinity. And use 'U' for the union symbol. Interval(s) of Continuity: Let f(x) = x - 1. Use interval notation to indicate where f(x) is continuous. NOTE: When using interval notation in WeBWorK, remember that: You use 'I' for infinity and '-I' for - infinity. And use 'U' for the union symbol. Interval(s) of Continuity:

Explanation / Answer

1) Note that F(x) is undefined when the denominator equals zero. Since the denominator of F(x) is, I am assuming, (x - 2)(x + 5), we see that F(x) is undefined when: x - 2 = 0 and x + 5 = 0 ==> x = 2 and x = -5. Therefore, since F(x) is defined and continuous for all x except 2 and -5, f(x) is continuous on (-infinity, -5) U (-5, 2) U (2, infinity). I hope this helps!

2)This function is continuous everywhere, because polynomials are defined everywhere. There are no restricted values as to what x cannot be.

This function is continuous over (-infinity, infinity)

3)Anything under a cube root sign is always continuos n R

Interval notation:
(-infinity, infinity)

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